adjacent vertices
vertices joined by edges
In a graph, adjacent vertices are vertices that are directly connected to each other by an edge. In other words, they are vertices that share a common edge.
For example, consider the following graph:
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A—-B
| |
| |
C—-D
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In this graph, vertices A and B are adjacent because they are connected by an edge. Similarly, vertices A and C are adjacent, vertices B and D are adjacent, and so on.
The concept of adjacent vertices is important in graph theory because it allows us to understand the relationships between vertices in a graph and how they are connected. This, in turn, can be used to solve problems related to graph theory, such as finding the shortest path between two vertices or identifying cycles in a graph.
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